<h2>题目编号 : 45</h2>
<div style="color:#666;font-size:80%;">06 June 2003</div><br />
<div class="problem_content">
<p>三角数、五角数和六角数由下列表达式生成：</p>
<table>
<tr>
<td>三角数</td>
<td>&nbsp;</td>
<td>T<img src="" style="display:none;" alt="_(" /><sub><i>n</i></sub><img src="" style="display:none;" alt=")" />=<i>n</i>(<i>n</i>+1)/2</td>
<td>&nbsp;</td>
<td>1, 3, 6, 10, 15, ...</td>
</tr>
<tr>
<td>五角数</td>
<td>&nbsp;</td>
<td>P<img src="" style="display:none;" alt="_(" /><sub><i>n</i></sub><img src="" style="display:none;" alt=")" />=<i>n</i>(3<i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' />1)/2</td>
<td>&nbsp;</td>
<td>1, 5, 12, 22, 35, ...</td>
</tr>
<tr>
<td>六角数</td>
<td>&nbsp;</td>
<td>H<img src="" style="display:none;" alt="_(" /><sub><i>n</i></sub><img src="" style="display:none;" alt=")" />=<i>n</i>(2<i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' />1)</td>
<td>&nbsp;</td>
<td>1, 6, 15, 28, 45, ...</td>
</tr>
</table>
<p>可以验证：T<img src="" style="display:none;" alt="_(" /><sub>285</sub><img src="" style="display:none;" alt=")" /> = P<img src="" style="display:none;" alt="_(" /><sub>165</sub><img src="" style="display:none;" alt=")" /> = H<img src="" style="display:none;" alt="_(" /><sub>143</sub><img src="" style="display:none;" alt=")" /> = 40755。</p>
<p>找到下一个即是五角数也是六角数的三角数。</p>

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